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lecture7 - Definitions Ambiguity and vagueness in ordinary...

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Definitions Ambiguity and vagueness in ordinary language can impede clear thinking and reasoning, and lends to some problems in logic. A word is ambiguous if it has more than one meaning. e.g. ‘bank’ can mean ‘financial institution’ and ‘river bank’. A word is vague if it admits of borderline cases : cases in which it neither clearly applies nor clearly does not apply. e.g. ‘bald’, ‘rich’, ‘mountain’, ‘person’.
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Problems with vagueness In fact, vagueness (in this technical sense) leads to notorious paradoxes. 1) Homer Simpson has two hairs on his head and is bald 2) If HS has n hairs on his head and is bald, then if HS had n+1 hairs on his head, HS is bald. So, 3) If HS has 3 hairs on his head then he is bald. But given (2) and (3), 4) If HS has 4 hairs on his head then he is bald. And we can repeat this line of reasoning as many times as we like. So we’ll end up with: If HS has 100,000,000 hairs on his head then he is bald. But this is obviously false.
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Definitions Clarity about the meanings of our terms helps to clear up some of this ambiguity and vagueness. This is where definitions come in. Definitions give the meaning of a word or phrase (term). But there are different ways of doing this and so different types of definition. Two ways of defining a term: (1) Give its extension : the set of things to which it applies. (2) Give its intension : the properties a thing must have to be included in the term’s extension. Ex. the extension of ‘Phil 3 TA’ is: Jon and Dan . the intension is something like: person who holds Phil 3 sections, grades work, etc
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Extensional definitions Two types of extensional definition: (1) Ostensive definition: that’s a graduate student; that’s a table, that’s the ocean, etc. (2) Verbal definition: ‘Baltic state’ means Estonia, Latvia or
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This note was uploaded on 03/14/2010 for the course PHIL 3 taught by Professor Way during the Fall '08 term at UCSB.

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lecture7 - Definitions Ambiguity and vagueness in ordinary...

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